Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces

被引：3

作者：

Wang, Yaqin ^{[1
,2
]}

Chen, Rudong ^{[3
]}

机构：

[1] Shaoxing Univ, Dept Math, Shaoxing 312000, Peoples R China

[2] Sichuan Univ, Math Coll, Chengdu 610064, Sichuan, Peoples R China

[3] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

来源：

FIXED POINT THEORY AND APPLICATIONS | 2011年

关键词：

hybrid method; accretive operator; variational inequality; pseudocontraction;

D O I：

10.1186/1687-1812-2011-63

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011) and Lu et al. (Nonlinear Anal, 71(3-4), 1032-1041, 2009).

引用

页码：1 / 9

页数：9

共 13 条

[1]

[Anonymous], NONLINEAR FUNCTIONAL

[2]

[Anonymous], ITERATIVE METHODS NO

[3]

[Anonymous], FIXED POINT THEORY A

[4] ZEROS OF ACCRETIVE OPERATORS [J].

DEIMLING, K .

MANUSCRIPTA MATHEMATICA, 1974, 13 (04) :365-374

[5] SOME GEOMETRIC PROPERTIES RELATED TO FIXED-POINT THEORY FOR NONEXPANSIVE MAPPINGS [J].

GOSSEZ, JP ;

DOZO, EL .

PACIFIC JOURNAL OF MATHEMATICS, 1972, 40 (03) :565-&

[6] Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces [J].

Jung, JS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 302 (02) :509-520

[7] NONLINEAR SEMIGROUPS AND EVOLUTION EQUATIONS [J].

KATO, T .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1967, 19 (04) :508-+

[8] Hybrid methods for a class of monotone variational inequalities [J].

Lu, Xiwen ;

Xu, Hong-Kun ;

Yin, Ximing .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (3-4) :1032-1041

[9]

Megginson R.E., 2012, An introduction to Banach space theory, V183

[10] Towards viscosity approximations of hierarchical fixed-point problems [J].

Moudafi, A. ;

Mainge, P. -E. .

FIXED POINT THEORY AND APPLICATIONS, 2006, 2006 (1)

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